A point charge Q is moving in a circular orbit of radius R in the xy-plane with an angular velocity $$\omega$$. This can be considered as equivalent to a loop carrying a steady current $${{Q\omega } \over {2\pi }}$$. A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant $$\gamma$$.
The change in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is
The mass of a nucleus $$_Z^AX$$ is less than the sum of the masses of (A-Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of masses m1 and m2 only if (m1 + m2) < M. Also two light nuclei of masses m3 and m4 can undergo complete fusion and form a heavy nucleus of mass M' only if (m3 + m4) > M'. The masses of some neutral atoms are given in the table below :
| $$_1^1H$$ | 1.007825 u | $$_1^2H$$ | 2.014102 u |
|---|---|---|---|
| $$_3^6Li$$ | 6.015123 u | $$_3^7Li$$ | 7.016004 u |
| $$_{64}^{152}Gd$$ | 151.919803 u | $$_{82}^{206}Pb$$ | 205.974455 u |
| $$_1^3H$$ | 3.016050 u | $$_2^4He$$ | 4.002603 u |
| $$_{30}^{70}Zn$$ | 69.925325 u | $$_{34}^{82}Se$$ | 81.916709 u |
| $$_{83}^{209}Bi$$ | 208.980388 u | $$_{84}^{210}Po$$ | 209.982876 u |
(1 u = 932 MeV/c2)
The correct statement is
The mass of a nucleus $$_Z^AX$$ is less than the sum of the masses of (A-Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of masses m1 and m2 only if (m1 + m2) < M. Also two light nuclei of masses m3 and m4 can undergo complete fusion and form a heavy nucleus of mass M' only if (m3 + m4) > M'. The masses of some neutral atoms are given in the table below :
| $$_1^1H$$ | 1.007825 u | $$_1^2H$$ | 2.014102 u |
|---|---|---|---|
| $$_3^6Li$$ | 6.015123 u | $$_3^7Li$$ | 7.016004 u |
| $$_{64}^{152}Gd$$ | 151.919803 u | $$_{82}^{206}Pb$$ | 205.974455 u |
| $$_1^3H$$ | 3.016050 u | $$_2^4He$$ | 4.002603 u |
| $$_{30}^{70}Zn$$ | 69.925325 u | $$_{34}^{82}Se$$ | 81.916709 u |
| $$_{83}^{209}Bi$$ | 208.980388 u | $$_{84}^{210}Po$$ | 209.982876 u |
(1 u = 932 MeV/c2)
The kinetic energy (in keV) of the alpha particle, when the nucleus $$_{84}^{210}Po$$ at rest undergoes alpha decay, is
A right-angled prism of refractive index $$\mu$$1 is placed in a rectangular block of refractive index $$\mu$$2, which is surrounded by a medium of refractive index $$\mu$$3, as shown in the figure. A ray of light e enters the rectangular block at normal incidence. Depending upon the relationships between $$\mu$$1, $$\mu$$2 and $$\mu$$3, it takes one of the four possible paths 'ef', 'eg', 'eh' or 'ei'.
Match the paths in List I with conditions of refractive indices in List II and select the correct answer using the codes given below the lists:
| List I | List II | ||
|---|---|---|---|
| P. | $$e \to f$$ |
1. | $${\mu _1} > \sqrt 2 {\mu _2}$$ |
| Q. | $$e \to g$$ |
2. | $${\mu _2} > {\mu _1}$$ and $${\mu _2} > {\mu _3}$$ |
| R. | $$e \to h$$ |
3. | $${\mu _1} = {\mu _2}$$ |
| S. | $$e \to i$$ |
4. | $${\mu _2} < {\mu _1} < \sqrt 2 {\mu _2}$$ and $${\mu _2} > {\mu _3}$$ |